Is it possible to show the product variations as a gallery and/or slideshow instead of the default dropdown menu? I have a store with single products that have a large number of color variations, and it's much easier for a customer to scan through a gallery of colors than to have to choose each individually in the drop down before they can see it.

I'm open to plugin/extension suggestions for this. I am not a coder, but do have a little basic knowledge and am willing to give it a go if that's the only solution.

You can always add all of the images of the colors to the product gallery of the main variable product. They will display and be visible just like any other simple product's gallery images would be displayed, before the user picks a variation.

The user would still have to drop down and choose the one they wanted after going through the gallery images.

I think what you're asking for is like, having an "add to cart" button on each individual image in a gallery.. I can't think of a way to do that with out of the box woocommerce, and I also don't know of a plugin that would do that.